Re: Non-Symmetric Energy Tensors and Kaluza Klein Experiment

Jay R. Yablon says...

After reviewing some very helpful discussion in prior threads regarding
non-symmetric energy tensors and a Kaluza-Klein experiment, and am
starting to shift my viewpoint to be in opposition to the idea of using
a non-symmetric (Cartan / Tortion) energy tensor because of the adverse
impact this has on formulating a metric theory of gravitation.

There is a *non-symmetric* energy tensor in equations (15.11) to (15.13)
of:

http://jayryablon.files.wordpress.com/2008/03/kaluza-klein-theory-and-lorentz-force-geodesics-60.pdf

It's a nice paper, but I just don't think that the section on intrinsic
spin is correct. You speculate that intrinsic spin is "velocity" in the
extra, rolled-up dimension (actually, it's momentum in the extra dimension,
p_5, since you have to multiply by mass to get a constant).
I don't see how that can possibly be correct.

Kaluza-Klein already associated p_5 with
electric charge, and we know that charge is unrelated to intrinsic spin.
Note that an electron's spin can be in two states: spin-up and spin-down.
If spin is associated with charge, then that would imply that flipping
the spin would flip the charge, changing an electron into a positron.
That is not observed.

We also know that an electron's spin state is *not* a constant.
Total angular momentum (the sum of spin angular momentum and
orbital angular momentum) is conserved, but spin by itself is
not. So there is a coupling between spin and ordinary, orbital
angular momentum. There is no such coupling between orbital
angular momentum and p_5.

Also, intrinsic spin has a *direction* in ordinary 3-space. A
particle has spin-up or spin-down relative to a particular
direction in 3-space. In contrast, p_5 has no relationship to
the other 3-space directions.

Putting these objections together with the already known
objection that neutrinos are neutral, but have intrinsic
spin, it would seem to me that there is no reason at all
for believing that p_5 has anything to do with intrinsic
spin. The fact that it is quantized is not evidence that
p_5 has to do with spin, it is evidence that p_5 is momentum
in a dimension that is *circular*. If 2 pi R is the distance
*around* the fifth dimension, then an electron's wavelength
lambda will necessarily be such that an integral number
of wavelengths fit in 2 pi R. So this leads to the
quantization condition

lambda = 2 pi R/n

or in terms of p_5,

p_5 = 2 pi h-bar/lambda = n h-bar/R

Since p_5 is proportional to Q/square-root(G),
this gives

Q = constant * n * h-bar * square-root(G)/R

If we set n=1 and Q=the charge on an electron,
this again gives R around a Planck length
(to within a factor of 10 or so).

I really think that associating the extra dimension
with intrinsic is barking up the wrong tree.

--
Daryl McCullough
Ithaca, NY

.

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